A Morse complex on manifolds with boundary (Q634711)

Given a Morse function on a compact smooth manifold \(M\) with non-empty boundary, the authors build a Morse complex whose homology is isomorphic to the (absolute or relative to the boundary) homology of \(M\) with integral coefficients. The construction uses a pseudo-gradient Morse-Smale vector field suitably adapted to the boundary. The approach of the authors simplifies the other methods which have been previously discussed in the literature in more specific geometric settings.